A certain sum amounts to ₹12,456 in 3
2
1
years at 8.5% p.a. simple interest. What will be the simple interest on the same sum in 6
4
1
years at the same rate of interest?
- A₹5,100
- B₹5,046
- C₹3,060
- D₹5,240
Solution & Step-by-step Explanation
Let the principal sum be P, the rate of interest be R=8.5%, and the first time period be T
1
=3
2
1
=
2
7
years.
The amount A
1
after T
1
years is given by:
A
1
=P+SI
1
=P+
100
P×R×T
1
12456=P(1+
100
8.5×
2
7
)
12456=P(1+
200
59.5
)=P(
200
259.5
)
P=
259.5
12456×200
=
259.5
2491200
=9600
So, the principal sum is ₹9,600.
Now, we need to find the simple interest (SI
2
) on the same sum for T
2
=6
4
1
=
4
25
years at the same rate R=8.5%:
SI
2
=
100
P×R×T
2
SI
2
=
100
9600×8.5×
4
25
SI
2
=96×8.5×
4
25
=24×8.5×25=24×212.5=5100
Thus, the simple interest is ₹5,100.
1
=3
2
1
=
2
7
years.
The amount A
1
after T
1
years is given by:
A
1
=P+SI
1
=P+
100
P×R×T
1
12456=P(1+
100
8.5×
2
7
)
12456=P(1+
200
59.5
)=P(
200
259.5
)
P=
259.5
12456×200
=
259.5
2491200
=9600
So, the principal sum is ₹9,600.
Now, we need to find the simple interest (SI
2
) on the same sum for T
2
=6
4
1
=
4
25
years at the same rate R=8.5%:
SI
2
=
100
P×R×T
2
SI
2
=
100
9600×8.5×
4
25
SI
2
=96×8.5×
4
25
=24×8.5×25=24×212.5=5100
Thus, the simple interest is ₹5,100.